Finite Group Databasebeta

← #11781194

Subgroups — #11781194

Order 1152.

268 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593749C211yesmaximal, characteristic
2#10593395C211yesmaximal, characteristic, complemented
3#10590433C212yesmaximal
4#10590042C211yesmaximal, characteristic, complemented
5#10590040C212yesmaximal, complemented
6C2×#3787—21no—
7#64102C2211yescharacteristic
8#63919C2212yes—
9#63778—21no—
10C4⋊#622C2211yescharacteristic
11C4×#622C2211yescharacteristic
12#63743—21no—
13#63743—21no—
14C3×#808—22no—
15#63572C2212yes—
16#63564—22no—
17#4870—62no—
18C2×C4⋊(C3⋊D3)D411yescharacteristic
19C2×C4×C3⋊D3—21no—
20C2×#627—22no—
21C2×#622—21no—
22C2×#622D411yescharacteristic
23C2×#622D411yescharacteristic
24#3787—42no—
25C32×C4⋊C4D411yescharacteristic
26#3752—21no—
27C4×C3⋊Dic3C2311yescharacteristic
28C3×C4⋊Dic3—22no—
29C2×C3×C3⋊C8—22no—
30#3724—22no—
31#1675—91nomaximal, Sylow
32#893—62no—
33#888—62no—
34C3×#106—62no—
35#821—62no—
36Dic3⋊C8—62no—
37#809—62no—
38#808—22no—
39C22×C3⋊D3—21no—
40C2×C32×C4—21no—
41C2×C32×C4C2×D411yescharacteristic
42C2×C3⋊Dic3C2×D411yescharacteristic
43C2×C3⋊Dic3#4111yescharacteristic
44C4⋊(C3⋊D3)—21no—
45C4⋊(C3⋊D3)Q1612yes—
46C4×C3⋊D3—41no—
47C4×C3⋊D3—41no—
48C2×C3×Dic3—42no—
49#627—82no—
50#622—21no—
51#622—41no—
52#622SD1612yes—
53C3×C3⋊C8—42no—
54#500—91no—
55#476—92no—
56C8×D4—91no—
57#335—91no—
58#333—92no—
59C2×D12—62no—
60C2×C4×D3—122no—
61C2×Dic6—122no—
62C2×C3×C8—62no—
63C3×C4⋊C4—22no—
64C3×C4⋊C4—62no—
65(C2×D3)⋊C4—122no—
66C4⋊Dic3—22no—
67Dic3⋊C4—122no—
68C4×Dic3—62no—
69C2×C3⋊C8—22no—
70C22×C32#12111yescharacteristic
71C2×C3⋊D3—22no—
72C2×C3⋊D3—41no—
73C2×C3⋊D3—41no—
74C32×C4—41no—
75C32×C4C2×Q1611yescharacteristic
76C32×C4#13511yescharacteristic
77C3⋊Dic3—21no—
78C3⋊Dic3C2×SD1611yescharacteristic
79C3⋊Dic3#13711yescharacteristic
80C3×Dic3—82no—
81C22×C8—181no—
82C4⋊Q8—92no—
83C4×D4—91no—
84#107—181no—
85#107—181no—
86#106—62no—
87C4⋊C8—92no—
88C4⋊C8—91no—
89#102—182no—
90C22⋊C8—181no—
91C4×C8—91no—
92C22×D3—122no—
93C2×C3×C4—22no—
94C2×C3×C4—42no—
95C2×C3×C4—122no—
96C2×Dic3—42no—
97C2×Dic3—62no—
98C2×Dic3—62no—
99D12—64no—
100D12—122no—
101C4×D3—242no—
102C4×D3—242no—
103Dic6—244no—
104C3×C8—122no—
105C3⋊C8—42no—
106C2×C32#46111yescharacteristic
107C2×C32#46711yescharacteristic
108C2×C32#47211yescharacteristic
109C3⋊D3—42no—
110C2×Q8—182no—
111C2×D4—91no—
112C22×C4—181no—
113C2×C8—62no—
114C2×C8—91no—
115C2×C8—91no—
116C2×C8—181no—
117C2×C8—362no—
118C4⋊C4—62no—
119C4⋊C4—182no—
120C4⋊C4GO+(4,𝔽2)11yescharacteristic
121C22⋊C4—181no—
122C42—91no—
123C22×C3—22no—
124C2×D3—124no—
125C2×D3—242no—
126C2×D3—242no—
127C3×C4—22no—
128C3×C4—22no—
129C3×C4—82no—
130C3×C4—242no—
131Dic3—62no—
132Dic3—62no—
133Dic3—82no—
134Dic3—122no—
135C32#167511yescharacteristic, complemented, Sylow
136C23—181no—
137Q8—722no—
138D4—92no—
139D4—181no—
140C2×C4—21no—
141C2×C4—91no—
142C2×C4—91no—
143C2×C4—122no—
144C2×C4—361no—
145C2×C4—361no—
146C2×C4C2×GO+(4,𝔽2)11yescharacteristic
147C8—92no—
148C8—122no—
149C8—181no—
150C8—361no—
151C2×C3—22no—
152C2×C3—22no—
153C2×C3—22no—
154D3—244no—
155C22—182no—
156C22—361no—
157C22—361no—
158C22#6424211yescharacteristic
159C4—41no—
160C4—91no—
161C4—91no—
162C4—181no—
163C4—242no—
164C4#6422311yescharacteristic
165C4#6422811yescharacteristic
166C3—22no—
167C2—362no—
168C2#1059344611yescharacteristic
169C2#1059346511yescharacteristic
170C2#1059347911yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C4⋊C4D4
socleC22×C32#121
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#1675
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10593395C2semidirect
4. #10590042C2semidirect
5. #10590040C2semidirect
135. C32#1675semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105937492
#105933952
#105904332
#105900422
#105900402
#16759